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~ STATISTICAl· PRIMER State Center for Health and Environmental Statistics
Department of Environment, Health, and Natural Resources • P.O. Box 29538 • Raleigh, NC 27626-0538 • 919/733-4728
No. 10
THE PARADOX OF PERCENT CHANGES
IN TOTAL VS. CATEGORY .. SPECIFIC RATES
March 1992
Population~based rates are routinely employed in public health to describe the natality, mortality, and
morbidity of various populations. By and large, we have become quite comfortable with the use of these rates.
However, when we proceed a step further and begin to speak of percent changes in the rates, we must remind
ourselves that percent changes depend upon a base level and consequently may not behave in ways we have
grown to expect.
Below are the 1989 live births and infant deaths for two race groups and for the total population. When the
infant mortality rate is computed for each of these columns (infant deaths divided by live births multiplied by
1000), we are not surprised to see that the total rate falls between the white and nonwhite rates:
1989
Total White Nonwhite
Infant Deaths 1,171 598 573
Live Births 102,091 68,455 33,636
Infant deaths per
1,000 live births 11.5 8.7 17.0
The total rate, in fact, must fall between the white and nonwhite rates since it is the weighted average of the two
rates as illustrated below:
(
8.7 X 6845~\
102091)
+ (17.0 X 33636)
102091
11.5
That race~specific and total rates behave this way, and do so consistently, may tempt us to expect
race~specific and total percent changes from one period to another to behave in a like manner, but this is not the
case. UPercent change" is an entirely different creature.

~ STATISTICAl· PRIMER State Center for Health and Environmental Statistics
Department of Environment, Health, and Natural Resources • P.O. Box 29538 • Raleigh, NC 27626-0538 • 919/733-4728
No. 10
THE PARADOX OF PERCENT CHANGES
IN TOTAL VS. CATEGORY .. SPECIFIC RATES
March 1992
Population~based rates are routinely employed in public health to describe the natality, mortality, and
morbidity of various populations. By and large, we have become quite comfortable with the use of these rates.
However, when we proceed a step further and begin to speak of percent changes in the rates, we must remind
ourselves that percent changes depend upon a base level and consequently may not behave in ways we have
grown to expect.
Below are the 1989 live births and infant deaths for two race groups and for the total population. When the
infant mortality rate is computed for each of these columns (infant deaths divided by live births multiplied by
1000), we are not surprised to see that the total rate falls between the white and nonwhite rates:
1989
Total White Nonwhite
Infant Deaths 1,171 598 573
Live Births 102,091 68,455 33,636
Infant deaths per
1,000 live births 11.5 8.7 17.0
The total rate, in fact, must fall between the white and nonwhite rates since it is the weighted average of the two
rates as illustrated below:
(
8.7 X 6845~\
102091)
+ (17.0 X 33636)
102091
11.5
That race~specific and total rates behave this way, and do so consistently, may tempt us to expect
race~specific and total percent changes from one period to another to behave in a like manner, but this is not the
case. UPercent change" is an entirely different creature.